Cortisone is a steroid that is applied to the skin to reduce inflammation. cortisone acts on cells within the dermis and can travel through unbroken epidermis to reach cells in the dermis. if the epidermis is such a good barrier, how can cortisone easily travel through it?

Cortisone is a steroid drug which is used to reduce the inflammation or swelling because it inhibits the release of those substance that cause inflammation and it also reduces the immune response.  

The cells in the body have cell membrane which is made up of phospholipid. Membrane absorb those substance easily which are lipid-soluble. So as cortisone is steroid hormone which is lipid-soluble therefore it easily diffuses through the cell membranes and reaches the cells within the dermis.  

Therefore the lipid solubility of cortisone allows it to travel through the epidermis of skin.